Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
23.3-a4
23.3-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.3
\( 23 \)
\( -23 \)
$14.79438$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 1 \)
$1$
$0.635600682$
0.820765345
\( \frac{36413212515684578678223}{23} a^{4} - \frac{26048650375034470290668}{23} a^{3} - \frac{153067823422492698650307}{23} a^{2} + \frac{65672136847671723793825}{23} a + \frac{127932477431619398226629}{23} \)
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -372 a^{4} + 226 a^{3} + 1434 a^{2} - 609 a - 1191\) , \( -5104 a^{4} + 2964 a^{3} + 20110 a^{2} - 7895 a - 16315\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-372a^{4}+226a^{3}+1434a^{2}-609a-1191\right){x}-5104a^{4}+2964a^{3}+20110a^{2}-7895a-16315$
529.13-a4
529.13-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.13
\( 23^{2} \)
\( - 23^{7} \)
$20.24275$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2 \)
$1$
$13.99550586$
1.44581672
\( \frac{36413212515684578678223}{23} a^{4} - \frac{26048650375034470290668}{23} a^{3} - \frac{153067823422492698650307}{23} a^{2} + \frac{65672136847671723793825}{23} a + \frac{127932477431619398226629}{23} \)
\( \bigl[a^{4} - 4 a^{2} + a + 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a + 1\) , \( 16 a^{4} - 226 a^{3} - 579 a^{2} - 466 a - 368\) , \( -29097 a^{4} - 15344 a^{3} + 86856 a^{2} + 37964 a - 21888\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}^{2}+\left(16a^{4}-226a^{3}-579a^{2}-466a-368\right){x}-29097a^{4}-15344a^{3}+86856a^{2}+37964a-21888$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.